The experimental setup and the analysis procedures were described in Refs. [1]}, [2]}, [3]}, [4]}
which used the same data set for other reaction channels (\(N\eta \) , \(N\pi ^0\) , and \(N\eta \pi ^0\) ) (most details were given in Ref.
[2]} for \(\eta \)  production, the most similar analysis was for \(\eta \pi ^0\)  pairs in Ref. [4]}.)
A detailed description of the present analysis will be given in a longer journal paper. Longitudinally polarized electron beams
(\(e^-\)  energy 1558 MeV) with polarization degrees between 83 and 85% produced circularly polarized bremsstrahlung photons.
The energy-dependent polarization \(P_{\odot }\)  of the photon beam followed from the polarization transfer formula given in
Ref. [7]} (see also [1]}, [2]}, [3]}, [4]}). The photons were energy tagged with
the Glasgow magnetic spectrometer [12]}.
The solid deuterated-butanol target contained longitudinally polarized deuterons (polarization degrees 55 - 62%).
The polarization of the bound nucleons was corrected for nuclear effects as in
Refs. [1]}, [2]}, [3]}, [4]}.
The detector was composed of the electromagnetic calorimeters Crystal Ball (CB) [17]} and TAPS [18]}
covering almost the full solid angle [1]}, [2]}, [3]}, [4]}. The target was placed in the
center of the CB.
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